# Questions tagged [dual-spaces]

The dual space of a vector space $V$ over a field $k$ is the vector space of all linear maps from $V$ into $k$.

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### Exercise 3.F.5 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler.

I am reading "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. 3.94 Definition dual space, $V'$ The dual space of $V$, denoted $V'$, is the vector space of all linear functionals on ...
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### Is $A\subset X$ bounded when $\{\Delta(x):x\in A\}$ is bounded for all $\Delta\in X^*$, $X$ is a normed space and $A\subset X$? [closed]

Let $X$ a normed space and $A\subset X$. Suppose that for all $\Delta\in X^*$, $\{\Delta(x):x\in A\}$ is bounded. Prove that A is bounded
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### Weak convergence and duals for $L_p$ involving time and probability space

Questions are from the theory of PDEs\SPDEs Question 1. Suppose $(V, H, V^\star)$ is a Gelfand triple (embeddings are continuous and dense, so $\|\|_H \le C \|\|_V$ for some $C>0$ etc) of ...
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Let $X$ a vectorial space y let $\Gamma \subset X^{\ast}$. We will say that $\Gamma$ is total in $X$ if $f(x)=0$, $\forall f \in \Gamma$ implies that $x=0$. I have to prove that if $\Gamma$ is total ...
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### the question of the formulation of the Dunford-Schwartz theorem about $l^{\infty}$

According to the book Dunford-Schwartz, Linear Operators I, Theorem IV.8.16 the space $(L^{\infty} (S, \Sigma, \nu))^*$ is isomorphic the space $ba (S, \Sigma_1, \| . \|)$. Unfortunately, I ran into ...
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